Compare the functions

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Compare the functions

Mathematics
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g(x) right? @freckles
let's play with it together

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Other answers:

do you know the range of sin(x) is -1 to 1 ?
Well I'm thinking 2 spots on the number line from -1 to 1. lol
so one of the following will give the min to f -3(-1)+2 -3(1)+2 so what is the min of f? notice the parabola h is in vertex form h=(x-h)^2+k where (h,k) is vertex k gives the min value of the function
and given that what is also the min of h?
the function h
sorry I should have recalled the x-coordinate of the vertex something else
h=(x-c)^2+k where (c,k) is vertex k gives the min value of this function
Ohh wait I totally read the question wrong! It asks for minimum, not maximum!
yep we want the smallest possible y per function
So f(x) is the greatest! Thank you :)
Wait no...hold on I'm redoing it.
you didn't answer my question of the two numbers I mentioned above for f can you tell me the smallest y value
really big hint: \[-1 \le \sin(x- \pi) \le 1 \\ \text{ multiply both sides by -3 } \\ 3 \ge -3\sin(x-\pi) \ge -3 \\ \\ \text{ add 2 on both sides } 3+2 \ge -3\sin(x-\pi)+2 \ge -3+2 \]
Oh they're all the same? So it's D?
yes -3+2 is the min of f and -1 is the min of g and -1 is also the min of h
-3+2=-1=-1
Ohhh okay! Thank you so much! :)

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